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All rights reserved. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688.

Library of Congress Cataloging-In-Publication Data

Higham, Nicholas J., 1961-
Accuracy and stability of numerical algorithms/Nicholas J. Higham.-
2nd ed.
p. cm.
Includes bibliographical references.

I. Numerical analysis-Data processing. 2. Computer algoriths. I.
Title
QA297 .H53 2002
519.4 ?-0285 ?5-dc2I

2002075848

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Dedicated to
Alan M. Turing
and
James H. Wilkinson

About the Dedication

This book is dedicated to the memory of two remarkable English mathematicians, James Hardy Wilkinson (1919-1986), FRS, and Alan Mathison Turing (1912-1954), FRS, both of whom made immense contributions to scientific computation.

Turing's achievements include his paper "On Computable Numbers, with an Application to the Entscheidungsproblem", which answered Hilbert's decidability question using the abstract device now known as a Turing machine [1164, 1936]; his work at Bletchley Park during World War II on breaking the ciphers of the Enigma machine; his 1945 report proposing a design for the Automatic Computing Engine (ACE) at the National Physical Laboratory [1165, 1945]; his 1948 paper on LU factorization and its rounding error analysis [1166,...